Are any transactions exempt from Strong Customer Authentication - will I always have to confirm it's me?

If your online purchase is considered low value or low risk, it's possible that you wont need to confirm it's you (you'll be prompted if you do need to). You may also find that recurring payments - a series of payments of the same value to the same merchant (e.g. subscriptions and membership fees) - are exempt after the initial setup. However they are not exempt where the amount changes each time, for example - a utility bill.